Bringing computation into the classroom

The use of computation in the physics classroom has the potential to revolutionise the teaching of many topics in the Physics curriculum. By allowing teachers to move beyond problems that can be solved by hand in the limited time available in a lecture, students can be given a much more authentic experience of the topic. With carefully scaffolded tasks, either in a lecture or in a dedicated computational lab, students can explore a much wider range of problems, in a more meaningful way. We will discuss our experience of using computational physics at Sydney, with emphasis on how to think about introducing it into your own teaching. We will discuss the types of problems that can be tackled, which tools to use, and how to deal with students with different background experience. Participants are asked to install the Anaconda python distribution before the workshop https://www.anaconda.com/products/distribution and bring along suggestions for parts of the curriculum you would be interested in exploring. Intended Audience: University physics educator

Dynamics of matter-wave solitons in a ratchet potential

We study the dynamics of bright solitons formed in a Bose-Einstein condensate with attractive atomic interactions perturbed by a weak bichromatic optical lattice potential. The lattice depth is a biperiodic function of time with a zero mean, which realises a flashing ratchet for matter-wave solitons. The average velocity of a soliton and the directed soliton current induced by the ratchet depend on the number of atoms in the soliton. We employ this feature to study collisions between ratchet-driven solitons and find that soliton transport can be induced through their interactions. In the regime when matter-wave solitons are narrow compared to the lattice period the ratchet dynamics is well described by the effective Hamiltonian theory.Comment: 4 pages, 5 figure

Concordance groups of links

We define a notion of concordance based on Euler characteristic, and show that it gives rise to a concordance group of links in the 3-sphere, which has the concordance group of knots as a direct summand with infinitely generated complement. We consider variants of this using oriented and nonoriented surfaces as well as smooth and locally flat embeddings

Self-trapped nonlinear matter waves in periodic potentials

We demonstrate that the recent observation of nonlinear self-trapping of matter waves in one-dimensional optical lattices [Th. Anker et al., Phys. Rev. Lett. 94, 020403 (2005)] can be associated with a novel type of broad nonlinear state existing in the gaps of the matter-wave band-gap spectrum. We find these self-trapped localized modes in one-, two-, and three-dimensional periodic potentials, and demonstrate that such novel gap states can be generated experimentally in any dimension

Asymmetric vortex solitons in nonlinear periodic lattices

We reveal the existence of asymmetric vortex solitons in ideally symmetric periodic lattices, and show how such nonlinear localized structures describing elementary circular flows can be analyzed systematically using the energy-balance relations. We present the examples of rhomboid, rectangular, and triangular vortex solitons on a square lattice, and also describe novel coherent states where the populations of clockwise and anti-clockwise vortex modes change periodically due to a nonlinearity-induced momentum exchange through the lattice. Asymmetric vortex solitons are expected to exist in different nonlinear lattice systems including optically-induced photonic lattices, nonlinear photonic crystals, and Bose-Einstein condensates in optical lattices.Comment: 4 pages, 5 figure

Melting of Discrete Vortices via Quantum Fluctuations

We consider nonlinear boson states with a nontrivial phase structure in the three-site Bose-Hubbard ring, {\em quantum discrete vortices} (or {\em q-vortices}), and study their "melting" under the action of quantum fluctuations. We calculate the spatial correlations in the ground states to show the superfluid-insulator crossover and analyze the fidelity between the exact and variational ground states to explore the validity of the classical analysis. We examine the phase coherence and the effect of quantum fluctuations on q-vortices and reveal that the breakdown of these coherent structures through quantum fluctuations accompanies the superfluid-insulator crossover.Comment: Revised version, 4 pages, 5 figures, Accepted for publication in Physical Review Letter